renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
new file mode 100644 (file)
index 0000000..18e2459
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_aaa.ma
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/rt_computation/cpms_aaa.ma".
+include "basic_2/dynamic/cnv.ma".
+
+(* CONTEXT_SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Forward lemmas on atomic arity assignment for terms **********************)
+
+(* Basic_2A1: uses: snv_fwd_aaa *)
+lemma cnv_fwd_aaa (a) (h): ∀G,L,T. ⦃G, L⦄ ⊢ T ![a, h] → ∃A. ⦃G, L⦄ ⊢ T ⁝ A.
+#a #h #G #L #T #H elim H -G -L -T
+[ /2 width=2 by aaa_sort, ex_intro/
+| #I #G #L #V #_ * /3 width=2 by aaa_zero, ex_intro/
+| #I #G #L #K #_ * /3 width=2 by aaa_lref, ex_intro/
+| #p * #G #L #V #T #_ #_ * #B #HV * #A #HA
+  /3 width=2 by aaa_abbr, aaa_abst, ex_intro/
+| #n #p #G #L #V #W #T0 #U0 #_ #_ #_ #HVW #HTU0 * #B #HV * #X #HT
+  lapply (cpms_aaa_conf … HV … HVW) -HVW #H1W
+  lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
+  elim (aaa_inv_abst … H) -H #B0 #A #H2W #HU #H destruct
+  lapply (aaa_mono … H2W … H1W) -W #H destruct
+  /3 width=4 by aaa_appl, ex_intro/
+| #G #L #U #T #U0 #_ #_ #HU0 #HTU0 * #B #HU * #A #HT
+  lapply (cpms_aaa_conf … HU … HU0) -HU0 #HU0
+  lapply (cpms_aaa_conf … HT … HTU0) -HTU0 #H
+  lapply (aaa_mono … H … HU0) -U0 #H destruct
+  /3 width=3 by aaa_cast, ex_intro/
+]
+qed-.